SOLUTION: I am a whole number between 40,000 and 50,000. When I am divided by 2, the asnwer is a perfect square. When I am divided by 3, the answer is a perfect cube. Who am I? I need

Question 44848: I am a whole number between 40,000 and 50,000. When I am divided by 2, the asnwer is a perfect square. When I am divided by 3, the answer is a perfect cube. Who am I?
I need to explain how I got this
Help
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I am a whole number between 40,000 and 50,000. When I am divided by 2, the asnwer is a perfect square. When I am divided by 3, the answer is a perfect cube. Who am I?
I need to explain how I got this
------------------------------------------------------
Let the number be #; then 40000<#<50000
When # is divided by 3 the result is a perfect cube, as follows:
#/3=y^3
Then #=3y^3
Put that into the inequality, as follows:
40000<3y^3<50000
Divide thru by 3 to get
13333.333< y^3 <16666.666...
Take the cube root from left to right to get:
23.7126...< y <25.5436...
Therefore y is either 24 or 25
Then #=3*24^3 or #=3*25^3
If #=3^24^3=41472
When we divide this by 2 we get 20736
If we take the square root we get 144.
So when 41472 is divided by 2 we DO get a perfect square.
And when we divide 41472 by 3 we DO get a perfect cube.
Could #=3*25^3 also be an acceptable answer?
#=3*25^3= 46875
When we divide by 2 we get 23437.5
which is not a perfect square.
So the number you are looking for is 41472.
Cheers,
Stan H.

RELATED QUESTIONS
I am a number between 1 and 500 When I am divided by 63 the remainder is 7 When I am... (answered by ankor@dixie-net.com)

I am thinking of a number between 40 and 100 when the number is divided by 8 the... (answered by Edwin McCravy)

a whole number between 40000 and 50000 when divided by 2 is a perfect square and divided... (answered by Alan3354)

I am thinking of a number, when divided by 9 the remainder is 4. When divided by 5 the... (answered by MathLover1,greenestamps)

i am a 5 digit number between 40 000 and 50 000. my thousands digit is 1 less than the... (answered by Edwin McCravy)

I am a 2 digit number. When I am divided by 2,3,4,5,6,7,8,9 or 10, the remainder is... (answered by ikleyn)

i am a number less than 10 when i am divided by 2 half of that number is also 2 what... (answered by fcabanski)

I am a three digit number less than 200. When I am divided by 2,3,6,7 and 9, there is a... (answered by Edwin McCravy)

I am thinking a number. when i divided that number by 1/2 I get 3 times my original... (answered by checkley77)